Thursday, September 3, 2009

He Shoots! He Scores!

When Bo got home from his basketball game last night, looking pretty pleased with himself, his roommates asked him how it went. He said that he had 10 rebounds, 2 blocks, 3 assists, and equaled or bettered his season high in points. Naturally they wanted to know exactly how many points he scored. Since he never likes to give them a straight answer, he told them the following:


• I didn't shoot any free throws.

• The number of 2-point baskets I made is more than twice the number of 3-point baskets I made.

• The number of 2-pointers I made is less than or equal to 8.

• My previous season high was 18 points.

Now the roommates had to do some thinking! Using t to represent the number of 3-pointers he made, g to represent the number of 2-pointers, and f to represent the number of free throws, write equations or inequalities to represent all of the information given above. You should have four statements.

1. Decide which of the four graphs below best represents the information given in the problem. Explain your choice carefully!

2. What are all of the possible point totals for Bo?






If you would like to see the image more clearly click on the graph you want to see.

4 comments:

  1. MR and AM



    • The number of 2-point baskets I made is more than twice the number of 3-point baskets I made.

    • The number of 2-pointers I made is less than or equal to 8.

    • My previous season high was 18 points.

    1. Graph “A” because if you divide the final number that the dotted line got to by two and you will get eight, then divide the bold line by three, for the 3-pointers, and you will get two, this would follow the guidelines in which the two pointers are more than half of the three pointers.
    2. Possibilities are 24,25, and 26

    ReplyDelete
  2. A.C and CCG
    1. Equaled or bettered last one
    2. No free throws
    3. 2 pointers=2x # of 3 pointers
    4. Number of 2 pointers=less than or equal to 8
    5. Previous: 18.

    T = g2 + x
    2 <_ 8
    X >_ 18
    G = t½ - x

    1. Graph A. If you look, the one solid line going up is at one point close to 8 a little more than double the dotted line, making those two g and t. And it’s obvious the one going straight up is f, due to there is no change in rate, and it’s at 0.
    2. 18-28. 8x2=16 4x3= 12 12+16=28

    ReplyDelete
  3. A.E.,
    G= 2 pointers
    T= 3 pointers
    1.F=0
    2.2g ≤ 8
    3.g> 2t
    4.Season score≥18
    I think it is Graph A because I used my statements above and tested it out on each graph. On some graphs, I immediately eliminated then because they did not make sense.

    ReplyDelete
  4. - Every student in class gives all students except themselves a V in class.
    - V is 1/16 of in.
    - V stack is 5’ 4’’


    1/16’’x = 5’4’’
    1/16’’x = 64’’
    (16/1)1/16x = 64(16/1)
    X = 1024
    1024 Valentines
    √1024 = 32
    32 students
    32 chocolate hearts

    I started with the equation stating if a valentine is 1/16 inches and all of them are stacked into a pile that is 5 foot 4 inches then the equation is 1/16’’x (x being the amount of valentines) equals 5’4’’. I got rid of 1/16 by dividing on both sides. X (number of valentines equaled. Then I did the square root of 1024 to see what divided it evenly to get the amount of kids in the class. So if the square root of 1024 is 32, there are 32 kids in class. Mr. Sweet should buy 32 chocolate hearts.

    - LW

    ReplyDelete